关于目前宇宙学方面的观测证据告诉我们，在大尺度上，宇宙中存在着非常小的各向异性。在本文中，我们试图研究具有各向同性物质分布的局部旋转对称（LRS）均匀Bianchi-I时空。这是在$f(\mathcal{R},\mathscr{L}_m)$重力框架内完成的。特别地，我们考虑一个非线性$f(\mathcal{R},\mathscr{L}_m)$模型，$f(\mathcal{R},\mathscr{L}_m)=\dfrac{1}{2}\mathcal{R}+\mathscr{L}_m^{\,α}$。此外，状态方程参数$ω$，这是在确定宇宙的当前阶段的重要材料是受约束的。为了约束模型参数和状态方程参数，我们使用了57个哈勃数据点和1048个Pantheon Ia型超新星数据样本。并且，对于我们的统计分析，我们使用Markoc Chain Monte Carlo（MCMC）模拟。此外，在所获得的参数值的帮助下，我们测量了我们的模型的各向异性参数。
英文摘要：
The observational evidence regarding the present cosmological aspects tells us about the presence of very little anisotropy in the universe on a large scale. Here, in this paper, we attempt to study locally rotationally symmetric (LRS) homogeneous Bianchi-I spacetime with the isotropic matter distribution. This is done within the framework of $f(\mathcal{R},\mathscr{L}_m)$ gravity. Particularly, we consider a non-linear $f(\mathcal{R},\mathscr{L}_m)$ model, $f(\mathcal{R},\mathscr{L}_m)=\dfrac{1}{2}\mathcal{R}+\mathscr{L}_m^{\,α}$. Furthermore, $ω$, the equation of state parameter, which is vital stuff in determining the present phase of the universe is constrained. To constrain the model parameters and the equation of state parameter, we use 57 Hubble data points and 1048 Pantheon supernovae type Ia data sample. And, for our statistical analysis, we use Markoc Chain Monte Carlo (MCMC) simulation. Moreover, with the help of obtained values of parameters, we measure the anisotropy parameter for our model.
Angular power spectra of anisotropic stochastic gravitational wave background: developing statistical methods and analyzing data from ground-based detectors
